${\left( {\dfrac{{\sqrt 2 }}{2}} \right)^m} < {\left( {\dfrac{{\sqrt 3 }}{2}} \right)^m}$     

${\left( {\dfrac{{\sqrt 2 }}{2}} \right)^m} > {\left( {\dfrac{{\sqrt 3 }}{2}} \right)^m}$     

$1 < {\left( {\dfrac{{\sqrt 2 }}{2}} \right)^m} < {\left( {\dfrac{{\sqrt 3 }}{2}} \right)^m}$           

${\left( {\dfrac{{\sqrt 2 }}{2}} \right)^m} > {\left( {\dfrac{{\sqrt 3 }}{2}} \right)^m} > 1$